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EDUC 242 Literacy Action Plan Stephanie Miller
Table of Contents
Introduction Page 1
Literacy Challenges in a Mathematics Classroom Page 2
Literacy Challenges in the 21st Century Page 2
Supporting Literacy in a Mathematics Classroom Page 3
Interest Inventory Page 6
Analysis of textbook Page 7
Pythagorean Theorem Lesson Plan Page 9
Triangle Congruence Lesson Plan Page 17
Trade Books for a Mathematics Classroom Page 24
Action Plan for Literacy Development Page 29
References Page 30
Literacy Action Plan Page | 1
According to the Common Core State standards, it will be my responsibility as a future
teacher to develop literacy inside my classroom (The Standards: English Language Arts
Standards). When I first heard about these literacy standards, I was opposed them. This was not
because I felt teaching literacy was solely the job of the English department. In fact, I approved
of the plan for students to develop literacy in a variety of subjects. My opposition of literacy
development inside my own classroom stemmed from that fact that I wish to teach mathematics.
Never had I heard of reading anything beyond a textbook inside a math classroom. Literacy in
the Content Areas has helped change my outlook on literacy development in my future
classroom by exposing me to a variety of teaching methods and trade books that can (and have)
been used in a mathematics.
Teaching literacy in a math classroom is important because it helps students become
“become independent learners capable of acquiring mathematics outside of school when the need
arises” (Lee & Spratley, 2009). The key for teaching literacy in any classroom is to get students
excited about reading and writing. According to the research article “Adolescent Literacy”
written by the James R. Squire Office of Policy Research, “Motivation can determine whether
adolescents engage with or disengage from literacy learning” (2007). To do this, I must have a
variety of genres and reading levels from which students can choose. This allows for students to
choose a reading that they would not consider too boring or too difficult. I must also choose
topics that are within a students’ schema. Students will be turned off if they are reading about a
topic they know nothing about. Vocabulary development is critical to teaching literacy because it
helps students understand what they are reading. When the students have made these new
vocabulary words their own, they will a larger vocabulary from which to draw when writing or
speaking.
Literacy Action Plan Page | 2
Although literacy development in a math classroom is possible, it is not without its
challenges. First, “math texts present special literacy problems and challenges for young readers”
(Lee & Spratley, 2009). Math is more than understanding the words on a page; it is practically
another language. The symbols and numbers seen in mathematics texts make them vastly
different then what readers see in other works. Teaching literacy in mathematics means
introducing students to this new language and developing their vocabulary and critical thinking
skills. Also, typical reading strategies may not aid comprehension when reading a math textbook.
These strategies, such as previewing, making predictions, and summarizing, “do not necessarily
help students to develop conceptual understanding, which comes only through repeated practice
with problem solving” (Lee & Spratley, 2009). As a math teacher, I need to introduce students to
a reading strategy that will work in a math classroom.
The major challenge is finding the time to address literacy. With rising teacher credibility
in high stakes testing, it is more important than ever that I make sure my students understand the
content. Meeting all of the math standards takes a lot of instruction and practice time. This hardly
leaves time to help students develop their reading and writing skills, which may seem unrelated
to the content if not incorporated well.
It is imperative that literacy is no longer limited to reading and writing. “It also extends to
new media—including non-digitized multimedia, digitized multimedia, and hypertext or
hypermedia” (Rotherham & Willingham, 2009). This brings with it certain challenges to student
literacy development in the 21st century. These challenges must be addressed in order to improve
the development of literacy in students.
Literacy Action Plan Page | 3
The first challenge is students must become proficient in a variety of literacies. Visual
literacy will be extremely important in my classroom. Math students will need to be able to
comprehend visuals, such as graphs and diagrams. I will be sure to pay particular attention to
helping students learn how to interpret these visuals as “it’s virtually impossible to open a
newspaper or news magazine without finding information in chart form or in symbols of some
sort” (Schultz, 2008). My students will be expected to analyze, interpret, and explain these
visuals often in the classroom.
A second challenge is for literacy development is learning how to use new technologies.
“Educational technology is changing faster than ever” (Interactive Classroom Technology,
2012). Not only is it important to have access to these technologies, but also it is essential for the
students to know how to use the technologies. Without this ability, students may fall behind their
peers in the job market. As a future teacher, I should be a leader of technology. This involves
active learning of these new devices, even if I feel current devices can achieve a job just as well.
A third challenge for students is learning when to apply these different literacies.
Approximately one-third of all students own a personal mobile device of some kind (Kenney,
2011). This even includes students in kindergarten. These communication devices allow students
develop their texting literacy. Often, this form of communication involves a very different style
of writing than what is required in the classroom. Students must learn to navigate a world where
different writing styles are appropriate. My role as a teacher is to help students develop their
academic writing skills through lessons and practice.
The first step toward supporting literacy in any classroom is to develop a literate rich
environment. “The classroom library is beginning to appear across the curriculum. Building a
classroom library becomes a means to showing students how content knowledge is acquired and
Literacy Action Plan Page | 4
also serves as a way for teachers to share their passion for learning” (Schultz, 2008). My
classroom library will contain a variety of texts for students to read. This does not just mean
providing different topics. Books of varying genres and reading levels will also be present. I will
also use a mathematics word wall, as it will help develop my students’ vocabulary.
Building relationships with students is also extremely important when developing
literacy. Students will need to know that I care about their interests. Students also need to build
respectful relationships with their fellow students. This helps create an atmosphere that facilitates
learning in general. When students are in an environment that promotes learning, it follows that
students will be more likely to engage in literacy development.
One aspect of teaching literacy that cannot be forgotten is the planning stage. It is vital
that my actions in the classroom be intentional. Every lesson and activity must serve a purpose,
and this includes literary instruction. Determining student interest through interest inventories
will help me decide what topics students have knowledge in and what topics a student would like
to learn more about (Kane, 2011, p. 35). I must be intentional about teaching reading and writing
strategies as well as vocabulary. Therefore, I will plan how I wish to include literary instruction
in my classroom.
As mentioned above, some reading strategies may not work well when reading a math
textbook. This does not mean that I should completely abandon these strategies however.
Instead, I must adapt those strategies or use different texts. An example of a modified reading
strategy is the THIEVES (Title, Heading, Introduction, Every first sentence, Vocabulary, End of
chapter questions, Summary) strategy. By simple changing the first “E” to stand for Examples,
this strategy can easily be applied to a mathematics textbook (Schultz, 2008).
Literacy Action Plan Page | 5
There are also many trade books and articles that can be used in the classroom. These
works make the application of reading strategies much easier. The SQ3R strategy (Survey,
Question, Read, Recite, and Review) can be easily be applied to articles. Novels will most likely
engage students more than a textbook. These texts are also better for facilitating and participating
in discussions and social interaction. These works can also expose students to a variety of styles
and genres (Kane, 2011, p. 130).
I need to make sure I do not ignore the importance of teaching writing, because this is a
large aspect of literacy. When teaching writing, I need to include instruction over the writing
stages. I plan on focusing on some of the characteristics of good writing, such as ideas,
organization, voice, and fluency. Finally, I should consider what kind of writing I would like my
students to use. Students could write a letter or research paper, or something else entirely. I will
probably have each of my students write in a journal about their math experiences, including
writing about their thought process while solving a difficult problem. This will help them not
only develop their writing, but also their mathematical vocabulary (Kane, 2011, pp. 189-209).
The final aspect of supporting literacy in my math classroom that should be considered is
how I should assess the literacy development of my students. Requiring students to write an
explanation for how they solved the problem will help me determine whether the students
comprehended the problem and vocabulary. Observing students as they explain how to solve a
problem to a fellow student may also serve as a way for me to assess a students’ literary
development. Finally, I could have students keep an ongoing record of their reading or writing in
a portfolio (Kane, 2011, pp. 294-303).
Miss Miller’s Interest Inventory
Welcome! We are about to embark on a journey together to explore the wonderful world of
calculus! Calculus is a useful subject that has many applications, but in order to make this journey
meaningful for you, I need to know where your interests lie. Please help me by filling out this
survey so I can make the semester as exciting as possible for you.
A. Below are some questions that can be answered using calculus. Circle one or two of the
questions you would be interested in exploring.
a. How do police officers know how fast a car was traveling right before a wreck when
no one was around to clock their speed?
b. Where did the formulas for the areas and volumes of geometric figures come from?
c. How does NASA know how much fuel to put in a shuttle to make sure it reaches
orbit?
d. How long will it really take to drain a pool since the force of the water is constantly
falling?
e. How do environmentalists calculate the approximate carrying capacity of a species?
f. What happens if we never stop adding numbers together? (Hint: the answer isn’t
always infinity)
g. What’s the difference between velocity and acceleration and why is that important?
B. Answer the following questions about yourself.
a. In general, how do you feel about math and why?
b. You have gone through many math classes to get to this point. What would you say
is your greatest strength when it comes to math?
c. When it comes to math, what is your greatest weakness?
d. What are some of your interests and hobbies?
e. Have you done any exploring of math on your own (i.e. researched a math related
topic or person, read a math related book or magazine, or purposely searched for
difficult math problems to solve)? If so, what was it that you did?
f. What career would you like to have when you are out of school?
Stephanie Miller
Textbook Analysis
EDUC 242
Analysis
Geometry: Concepts and Skills is a textbook published by McDougal Littell in 2003. This
textbook covers the basics of geometric concepts. The book begins with the properties of lines
and angles. It moves on to talk about polygons, most specifically triangles, circles, and
quadrilaterals. There is also an introduction to trigonometry in a later chapter.
This textbook is organized very well, with the sections being very clearly labeled. The sections
and chapters begin with simple, specific ideas and builds to more complex ideas. For example,
the chapters on triangles and quadrilaterals appear before the chapter on polygons appears. As a
result, it seems the chapters and sections seem to build off each other in a logical way.
This textbook has some very useful features. Before each chapter, there is a study guide.
This provides students with a summary of what they are supposed to gain from the chapter.
There is also a chapter readiness quiz, which allows a teacher to assess whether the students have
the necessary skills to do well in the chapter. At the end of the chapter is a long review
assignment, which covers all of the skills a student should have learned in the chapter. In
addition, there is an algebra review at the end of every chapter. Throughout the textbook, there
are various suggestions for games, projects, and activities for the students to do. These
suggestions connect very well with the topics that are covered. For example, there is an activity
which explores the proof of the Pythagorean Theorem immediately before the introduction of the
theorem (Boswell, Larson, & Stiff, 2003, p. 191).
The clarity of the examples is impressive, but the quality of the content leaves much to be
desired. The examples are clear and concise. The figures that are included only enhance the
examples. Unfortunately, the sections do not provide much connection to the student. There is
also little description of the overall concepts. For example, the only description of the Side-Side-
Side Similarity Theorem that is given is that it a method “to show that two triangles are similar”
(Boswell et al, 2003, p. 379). As a teacher, I would want my students to have a more thorough
knowledge of the concepts than what the textbook provides.
The level of thinking required for the questions is relatively low. Most of the questions at
the end of the sections and chapters simply replicate examples provided. There are a few
questions for each chapter that extend beyond the examples, which are more thought-provoking.
In conclusion, this textbook is well organized, provides clear examples, and includes
helpful activity ideas. However, I do not feel this textbook challenges the reader to go to a deeper
lever of thinking. It also gives very little description if the concepts being covered. As a result,
this textbook is a great tool for teachers to have on hand for ideas, but it should not be used as the
classroom textbook.
Work Cited
Boswell, Laurie, Larson R., Stiff, L. (2003) Geometry: Concepts and Skill. Evanston, IL:
McDougal Little.
Fry Readability Test
p. 212 (I did not include the headings in my text)
“The diagrams below show a relationship between the longest and shortest sides of a triangle and
the largest and smallest angles. If one side of a triangle is longer than another side, then the angle
opposite the longer side is larger than the angle opposite the shorter side. If , then
. If one angle of a triangle is larger than another angle, then the side opposite the
larger angle is longer than the side opposite the smaller angle. If then .
Name the angles from largest to smallest. , so . Also, , so
. The order of…”
Number of syllables: 158
Number of sentences: 8+(3/13) 8.23
p. 230 (I did not include the headings in my text)
“A soccer goalie instinctively imagines a triangle formed by the goal posts and the ball. The best
position to stand allows the goalie to reach each side of the triangle in the same amount of time.
As the ball moves and the shape of the triangle changes, the goalie’s best position also changes.
You will learn more about soccer in Exercises 21 and 22 and p. 278. Facilities planners help
businesses determine the best locations for new buildings. They can help companies save money
and run more efficiently. Type designers design fonts that appear in books, magazines,
newspapers, and other…”
Number of syllables: 154
Number of sentences: 6+(12/13) 6.92
p. 452
“A circle is a set of all points in a plane that are the same distance from a given point, called the
center of the circle. A circle with center is called “circle ,” or The distance from the
center to a point on the circle is the radius. The plural of radius is radii. The distance across the
circle, through the center, is the diameter. The diameter is twice the radius r. So The
circumference of a circle is the distance around the circle. For any circle, the ratio of the
circumference to its diameter…”
Number of syllables: 145
Number of sentences: 8+(11/20) 8.55
Results
Average sentences: (8.23+6.92+8.55)/3=7.9
Average syllables: (158+154+145)/3 152.33
Fry Grade level: 8th
grade*
*This is a different result than what I got the first time because I miscounted one of my passages.
I do agree with the Fry Readability results. When flipping through the textbook, I felt that
the reading level was a little low for geometry students. Most students taking a geometry class
will be in the ninth or tenth grade. The Fry Readability test showed that the reading level is
approximately at the eighth grade level, although it is close to the seventh grade level. Because
the test agreed with my first impression of the textbook, I think the results are fairly accurate.
Lesson Plan by Stephanie Miller
Lesson: Pythagorean Theorem and Distance Formula
Length: 45 minutes
Grade: Geometry
Academic Standards:
MA.G.1.1 2000| Find the lengths and midpoints of line segments in one- or two-dimensional
coordinate systems.
MA.G.5.1 2000| Prove and use the Pythagorean Theorem.
Performance Objectives:
1) Given thirteen problems, the geometry students will apply the Pythagorean Theorem to
determine the length of the side of a right triangle at least 11 times correctly.
2) Given 5 problems, the geometry students will apply the Distance Formula to determine the
length of a line segment at least 4 times correctly.
Assessment:
Students will be assigned 18 problems (pp. 195-197 #2-36 evens) which will be solved correctly
with at least 83% accuracy.
Advance Preparation by Teacher:
1) Print off note taking guide for each student.
2) Open PowerPoint labeled “Pythagorean Theorem”
Procedure:
Introduction: “Previously, we have been working on isosceles and equilateral triangles and their
many properties. Could anyone tell me the difference between an isosceles and equilateral
triangle? (Answer: An equilateral triangle’s sides are all equal, an isosceles triangle has only two
congruent sides. Both have all acute angles) Today we will be moving on to right triangles. What
we are about to learn today is probably one of the most important concepts in mathematics. In
fact, you benefit from this concept every day because it plays a big part in making sure buildings
and bridges do not collapse from lack of support.”
Step by Step Plan:
1. Hand out note taking guide for section 4.4 to the students.
2. [Second slide] “We will begin today by going over a few terms that you need to know in
order to better understand the lesson.”
3. [Third slide] “Since we are talking more today about right triangles, it is important to know
the difference between a leg and a hypotenuse.”
4. Call on student to read the definition of “leg” aloud.
5. Call on a different student to read the definition of “hypotenuse” aloud.
6. [Press enter] “Now that we know the definition of a leg and hypotenuse, can anyone tell me
which side is the hypotenuse?” (Bloom’s Knowledge, Answer: side labeled “c”)
7. “Correct, side “c” is the hypotenuse because it is opposite the right angle. Sides “a” and “b”
are legs because they help form the right angle.
8. [Fourth slide] “Okay, now you have an understanding of the terminology, we are moving on
to learn about the Pythagorean Theorem.”
9. [Fifth slide] “This is the type of story problem we will be working on solving today.”
10. Ask a student to read the problem aloud.
11. “Now, let’s set this problem up.”
12. [Sixth slide] “Here, we have a boat on a lake.”
Lesson Plan by Stephanie Miller
13. [Press enter] “We drop the over the side of the boat and allow a little bit of slack. Notice there
is some extra chain length. Because of this extra chain length, the boat is able to drift
slightly”
14. [Press enter] “Eventually though, the chain is pulled taut, creating a straight line. Can anyone
see the shape we have created?” (Answer: right triangle)
15. [Press enter] “Exactly! We have created a right triangle. The dotted lines represent the legs of
the triangle.”
16. “How long is this leg that goes straight down?” (Answer: 19 feet) Note: Many will probably
answer 16 feet because that is how deep the lake is, but the chain went over the edge of the
boat, which is 3 feet above the surface of the lake.
17. [Press enter] “What is the name of this long side of the triangle?” (Bloom’s Knowledge,
Answer: hypotenuse)
18. “And how long is the hypotenuse?” (Answer: 21 feet) Note: Student may struggle to answer
this question.
19. [Press enter] “Yes, this hypotenuse actually represents the total amount of chain that was let
out, which means it includes the 19 feet of chain needed to hit the bottom and the additional
two feet of slack.”
20. [Press enter] “What we don’t know, but want to find out is how far we drifted. The distance
traveled is represented by this top leg of the triangle, which we will label “b””
21. [Seventh slide] “This is the same triangle we just created, without the background pictures.
We will be able to use what we learn today to determine the length of “b,” or how far the boat
drifted. As you listen to the rest of the lesson, try to figure out what you could do to solve this
problem because we will come back to it later.”
22. [Eighth slide] “Everyone get out a sheet of graph paper and a straightedge. If you do not have
a straight edge, use the side of your paper. Draw a right triangle with legs of 3 units each. For
each side, draw a square where one side of the square shares a side with the triangle.” Note:
This may have to be demonstrated for one side. (Gardener: Visual-Spatial)
23. “Once you have done that, see if you can find the relationship between the areas of the
squares that you drew. Then, using a different sized right triangle, test to see if the
relationship holds true for that triangle as well.”
24. Allow time for students to complete this activity.
25. “What did you find?” (Bloom’s Analysis, Answers will vary, but should be along the lines
that the area of the squares of the legs sum up to the area of the square of the hypotenuse)
26. [Ninth slide, press enter] “So when you add the size of the two smaller squares, you get the
size of the larger square.”
27. [Press enter] “Looking at this picture, the area of square with side length “a” has an area of a
squared and the area of square with side length “b” has an area of b squared. Adding them
together gives you the area of square with side length “c” which is c squared.”
28. [Press enter twice] “Thus, we have the relationship “a” squared plus “b” squared equals “c”
squared.”
29. [Tenth slide] “With this activity, we have actually just defined the Pythagorean Theorem.”
30. Ask student to read the theorem aloud.
31. [Eleventh slide] “Now let’s use this theorem we just learned.”
32. [Twelfth slide] “The easiest type of problem is to use the theorem to determine the length of
the hypotenuse.”
33. [Press enter] “The first step when using this formula is to determine where the hypotenuse is.
The theorem stated it only applied to right triangles. For what reason do you think there is a
rule that we can only use right triangles? (Bloom’s Synthesis, Answer: Hypotenuses only
exist on right triangles) Note: Students’ attention may need to be reverted back to the first
step in order to answer this question.
34. [Press enter] “The next step is to set up the formula. It might be easier for you, while you are
still learning the formula, to first write it down then substitute in the numbers for the
problem”
Lesson Plan by Stephanie Miller
35. [Press enter] “The third step is to solve for the unknown variable. This will sometimes
include some algebra.”
36. [Press enter] “The last step is the conclusion. For the conclusion simply write the answer in
the context of the problem and include the proper unit.”
37. [Thirteenth slide] “Alright, let’s try it. Find the length of the hypotenuse for the given
triangle.”
38. [Press enter] “Step 1: Determine which side is the hypotenuse. So which side is the
hypotenuse?” (Answer: side labeled “x”)
39. [Press enter twice] “Step 2: Set up the formula. So we are going to start with “a” squared plus
“b” squared equals “c” squared.”
40. [Press enter] “We know that “c” is the hypotenuse which we just determined is the side with
length “x,” so we can replace “c” with “x.” For the legs, we will let 4 represent “a” and 3
represent “b.” Keep in mind that you could switch it and make 4 be “b” and 3 be “a.””
41. [Press enter] “Step 3: Solve for the unknown, which is “x” in this problem.”
42. [Press enter] “Here’s our formula. We are going to square 4 and 3.”
43. [Press enter] “Now we have 16+9=x squared. Add these two numbers together.”
44. [Press enter] “25=x squared. Now we need to get rid of the squared, so we take the square
root…”
45. [Press enter twice] “…and we get x=5.”
46. [Press enter] “Step 4: Conclusion. So we say…”
47. [Press enter] “The length of the hypotenuse is 5 units long”
48. [Fourteenth slide] “Now let’s move on to another type of problem, find the length of the leg
of a triangle. We will use the same steps that we just used.”
49. [Press enter] “Which side is the hypotenuse?” (Answer: side with length “6”)
50. [Press enter twice] “So if we are going to set up the formula, what would we put as our “c?””
(Answer: 6)
51. “What would we put for our “a?”” (Answer: “x” or “5”)
52. [Press enter] “And we would make the other side be our “b.” So we have “x” squared plus 5
squared equals 6 squared.” Note: If students said “5” in step 53, they may have a different
order. This does not matter.
53. [Press enter twice] So now we solve for the unknown. Let’s square 5 and 6.
54. [Press enter] Now subtract 25 from both sides.
55. [Press enter twice] And to get rid of the square we take the square root of both sides.
56. [Press enter twice] So we have x=the square root of 11 which is approximately 3.32.
57. [Press enter] “And our conclusion is…”
58. [Press enter] “The length of the unknown side is approximately 3.32 units.”
59. [Fifteenth slide] “You need to be careful because there are a few common mistakes students
make when using this formula. First, students apply the formula when it is not a right triangle.
Second, sometimes students let their unknown always be “c” instead of reserving “c” for the
hypotenuse. Third, sometimes students forget to get rid of the square to get the unknown by
itself. Doing any of these will give you a wrong answer, so be careful.”
60. [Sixteenth slide] “Now we are going to talk about the Distance Formula.”
61. [Seventeenth slide] “If you have a point A on the coordinate plane at x sub one, y sub one,
and you have a point B at x sub 2, y sub 2, and you want to find the distance between them
you use the following formula: The length of line segment AB is equal to the square root of
the quantity x sub 2 minus x sub 1 squared minus the quantity y sub 2 minus y sub 1
squared.”
62. [Eighteenth slide] “Here I will show you what that means geometrically. We have a
coordinate plane with two points, A and B, and we want to find the length of the line segment
that connects them, which is also the distance between them. What we do is make this line the
hypotenuse of a right triangle.”
63. [Press enter] “We can easily find to length of these legs. To find the bottom leg, we simply
find the difference between the x coordinates. To find the length of the side leg, we simply
find the difference of the y coordinates.”
Lesson Plan by Stephanie Miller
64. [Press enter] “How would you solve for this unknown side using what we have learned
today?” (Bloom’s Application, Answer: Pythagorean Theorem)
65. [Press enter] “Now that we have a triangle, and the length of the two legs, we can solve for
the length of the hypotenuse using the Pythagorean Theorem.”
66. [Press enter] “So we have “a” squared, which is x sub 2 minus x sub 1 and “b” squared,
which is y sub 2 minus y sub 1 equals AB squared.
67. “Can anyone see how this equation is related to the Distance Formula?” (Bloom’s Analysis,
Answer: They are the same once we get rid of the exponent on the left side)
68. [Press enter] “Exactly, taking the square root of both sides gives us the Distance Formula.”
69. [Nineteenth slide] “Alright, so let’s do a quick example.”
70. [Twentieth slide] “Find the difference between points F and G.”
71. [Press enter] “First, plot the points and the line between them.”
72. [Press enter] “So we have point F in red at (0,1) and point G in blue at (3,3) and a black line
that connects them.”
73. [Press enter] “Now add legs to make a right triangle.”
74. [Press enter] “So we added this red line and this blue line from the points F and G to create a
right triangle.
75. [Press enter] “Finally, use the Distance Formula.”
76. [Press enter] “We have line segment FG is equal the square root of the quantity x sub 2 which
is the x coordinate of our G point minus x sub 1 which is the x coordinate of our F point
squared plus the quantity of y sub 2 which is the y coordinate of G minus y sub 1 which is the
y coordinate of F. Now let’s simplify.”
77. [Press enter] “We subtracted 3 minus 1 and 3 minus zero. Now square those numbers.”
78. [Press enter] “So we have 2 squared plus 3 squared under the square root. Square them.”
79. [Press enter] “Now we have under the square root 4 plus 9.”
80. [Press enter] “This gives us the square root of thirteen which is approximately…”
81. [Press enter] “3.61.”
82. [Twenty-first slide] “Ok, so now you should have a pretty good idea of how to use the
Pythagorean Theorem and Distance Formula, so let’s go back to our original problem
statement, which is on your note guide.”
83. [Twenty-second slide] “Every find a partner and see if you can figure out the distance the
boat drifted. When you figure it out, show your work on the board and take a seat.”
(Gardener: Interpersonal and Logical-Mathematical)
84. Allow time for students to solve the problem. Check each groups answer. (Answer: square
root of 80 which is approximately 8.94) Ask them either how they arrived at the correct
answer or where they found difficulties.
85. [Twenty-third slide] “Are there any questions? If not, here is the assignment due tomorrow.
Please get started on it. If you have any questions, please raise your hand, and I will come to
you.”
Closure:
2 or 3 minutes before dismissal, ask students to use a scratch piece of paper to write down the
Pythagorean Theorem and Distance Formula without looking at their notes or book. This is
not for a grade; it is to help them memorize the formulas because they will use them often in
the future.
Adaptations/Enrichments:
Student with a learning disability in mathematical calculation: The visuals for the opening
problem should make the student understand how the triangle we used to solve the
problem came from a real-world situation. Providing the students with a step by step
instruction should make it easier for them to solve the problems.
Student with ADHD: Giving the students an activity and a chance to get up to write on the board
will keep them from getting bored as easily and therefore, less likely distracted during the
lesson.
Lesson Plan by Stephanie Miller
Student with Gift/Talents in Math: Instead of solving #’s 2 and 4, ask student to use what he or
she has learned today to explain how they would find whether any triangle was a right
triangle or not, given all of the lengths of the sides. (Answer: See if the Pythagorean
Theorem still applies.) Ask them to come up with their own problem using the
Pythagorean Theorem if they get done early.
Self-Reflection:
Did the students seem to understand how to do the problems, or did they depend on my help?
Was there something I could have explained better?
Did the activity seem to help the students understand the concept?
Section 4.4: Pythagorean Theorem and the Distance Formula
Vocabulary
Leg:
Hypotenuse:
The Pythagorean Theorem
Problem Statement: When dropping an anchor, you are supposed to allow a little slack in
the chain once you feel the anchor hit the bottom. Your dad tells you to drop the
anchor over the side of the boat when his depth finder says the lake is 16 feet
deep. You estimate that the side of the boat is 3 feet above the lake surface and
you let out 2 extra feet of slack. Later, the chain is pulled tight because you have
drifted. How far away is your boat from where you originally dropped the anchor?
Set-Up:
Draw a picture:
With Background Without Background
Activity
Results:
1)
2)
Pythagorean Theorem:
Application:
How to solve a problem with Pythagorean Theorem:
Step 1:
Step 2:
Step 3:
Step 4:
Example 1: Find the length of the hypotenuse of a right triangle with the given sides.
Step 1:
Step 2:
Step 3:
Step 4:
Example 2: Find the length of the unknown side of the right triangle.
Step 1:
Step 2:
Step 3:
Step 4:
Common mistakes
1)
2)
3)
The Distance Formula
Distance Formula:
Geometric interpretation:
Application
Example 1: Find the distance from points F(1,0) and G(3,3).
Step 1:
Step 2:
Step 3:
Return to Problem Statement
Work:
Assignment:
Lesson Plan by Stephanie Miller
Lesson: Congruence and Triangles
Length: 35 minutes
Grade: Geometry
Academic Standard(s):
MA.G.4.6 2000| Prove that triangles are congruent or similar and use the concept of
corresponding parts of congruent triangles.
EL.CMP.3.1 2006| Demonstrate control of grammar, diction, paragraph and sentence
structure, as well as an understanding of English usage.
Performance Objective(s):
1) Given 18 problems, the geometry students will apply the concept of corresponding
parts to determine whether two triangles are congruent or not at least 15 times
correction.
2) When given a prompt, the geometry students will demonstrate their control of
grammar and paragraph structure by scoring at least 10 out of 12 points on a rubric.
Assessment:
Students will be assigned 18 problems (pp. 236-239 #16-50 evens) which will be solved
correctly with at least 83% accuracy.
Students will be assigned to write a paragraph summarizing the lesson with at least 83%
accuracy. Their paragraph will be graded for proper paragraph structure, grammar, and
accuracy of the content.
Advance Preparation by Teacher:
1) Make copies of note-taking guide for students.
2) Cut out enough triangle shapes for each student.
3) Post a sign that says “Congruent” and one that says “Not Congruent” on opposite
sides of the classroom.
4) Open PowerPoint labeled “Congruence and Triangles.”
Procedure:
Introduction: “Last chapter, we learned a lot about triangles, such as finding the length of
the sides and finding out the longest and shortest sides by using the angles. Today, we
will continue on the topic of triangles, but this chapter will be all about determining if
two triangles are the same or what mathematicians like to say, congruent. I found a video
on YouTube which introduces most of the topics we will be covering in this chapter.
While you are listening, write down some of the topics that are mentioned. Keep this
sheet and refer back to it throughout the chapter. By the end, you should be able to
explain almost everything that you wrote down.”
Lesson Plan by Stephanie Miller
Step by Step Plan:
1. [Slide 1] Hand out note-taking guide for each student.
2. Begin with introduction (above).
3. [Slide 2] Play video on PowerPoint.
4. Ask students to name off some of the topics they heard during the song. Topics
should include: SSS, SAS, ASA, AAS, HL, CPCTC, Congruence, and Corresponding
Parts.
5. [Slide 3] Explain to students that they will be using the concepts of congruence and
corresponding parts today.
6. [Slide 4] Call on students to read the definitions aloud. Ask students to try to draw
two congruent triangles based on the definition. Ask one student to draw their
triangles on board. (Gardener: Visual-Spatial) Ask class to classify the triangles based
on what they’ve learned in Chapter 4. (Bloom’s: Comprehension) Discuss whether
the triangles match the definition.
7. [Slide 5] Explain that there are specific notations to show congruence. [Press enter]
Describe the symbol for congruence, angles, and how congruent angles are shown.
[Press enter] Describe how congruent sides are shown on a triangle. [Press enter]
Describe the symbol for triangles and how congruent triangles are depicted. Be sure
to emphasize the order of the letters.
8. [Slide 6] Explain that the students will need to be able to write congruence
statements. [Press enter] The first is to determine whether the triangles are in fact
congruent by looking for corresponding parts. [Press enter] As each of the
corresponding angles and sides are highlighted, draw attention to the symbols that
indicate they are congruent. The next step is to list the letters of the angles in so the
corresponding angles are in the same order. [Press enter] Show how A is congruent
with F and both are listed forth, and so on.
9. [Slide 7] Tell students it is time for them to try. They will be shown two triangles and
they should shout out if they think they are congruent or not congruent.
10. [Slide 8] Give class time to answer. (Answer: Congruent) [Press enter] Give class
time to answer. (Answer: Congruent) [Press enter] Give class time to answer
(Answer: Not congruent).
11. [Slide 9] Pass out a triangle to each student and tell them to wander around the
classroom while the music plays. When the music stops, tell them to go up to the
student closest to them and determine whether their triangles are congruent or not.
They should go to the appropriate side of the classroom and the teacher should check
for accuracy. Ask various students with non-congruent triangles to identify the parts
that keep the triangle from being congruent. Repeat at least twice, where the third
time they switch triangles with someone. Have students return to their seat.
(Gardener’s: Bodily-Kinesthetic, Interpersonal; Bloom’s: Analysis)
12. [Slide 10] Tell students it is time to do some examples.
Lesson Plan by Stephanie Miller
13. [Slide 11] Ask a student to the question aloud. Be sure they say “Find the length of
line segment of XZ, and find the measure of angle Q.” Remind them that we know
the two triangles are congruent. Ask them how they could determine the length of the
line segment. (Bloom’s: Evaluation) [Press enter] They would use the fact that the
triangles are congruent to locate the corresponding parts. “Can you find the
corresponding angles?” (Bloom’s: Knowledge)
14. [Press enter three times] “If line segment PR has a length of 10, and PR is congruent
to line segment XZ, how long is line segment XZ?” (Answer: 10) [Press enter] “If
angle Y is 95 degrees, and angle Q is congruent to angle Y, what is the measure of
angle Q?” (Answer: 95 degrees) [Press enter]
15. [Slide 12] Read the problem aloud. [Press enter] Ask them to recall that vertical
angles are congruent. [Press enter] Ask them what it the arrows mean (Answer:
parallel lines). “There is a line that cuts through those lines. What is that line called?
(Answer: transversal). What do we know about the interior angles created by a
transversal?” (Answer: they are congruent). [Press enter twice]
16. [Slide 13] Summarize what was just discussed. [Press enter twice] Ask if they are
congruent (Answer: Yes, because the corresponding parts are congruent). [Press
enter] Discuss how they would write the congruence statement. [Press enter]
17. [Slide 14] Tell students to write a paragraph discussing what they have learned.
Remind them the structure should start with a thesis statement, include supporting
sentences relevant to the thesis statement, and should end with a statement that
summarizes what was said. Tell them they will be graded on accuracy, grammar, and
paragraph structure (Gardener’s: Linguistic). They will also have homework
problems which they can work on if they get done early, which will be due the next
class.
Closure: With five minutes remaining, have two students share what they wrote. Ask
class if they included something the two students shared.
Adaptations/Enrichments:
Students with a learning disability in mathematical calculation: The activity should
provide concrete examples to help the students understand the concept of
congruence. The emphasis on matching corresponding angles should provide the
students with an easy to follow guideline to determining whether the triangles are
congruent.
Students with ADHD: Giving the students an activity and a chance to get up to move
around will keep them from getting bored as easily and therefore, less likely to get
distracted during the lesson.
Lesson Plan by Stephanie Miller
Students with Gift/Talents in math: Instead of solving #’s 26, 28, and 30, ask students to
find patterns for the smallest amount of information they need to determine if the
triangles are congruent.
Self-Reflection:
Did the students need more help or time to write the paragraph?
Did the activity seem to help the students understand the concept?
What could I have explained better?
Sources:
Chandler, Laura. "Toe to Toe Geo." Teaching Resources. www.laurachandler.com. Web.
12 Apr.
2012. <http://www.lauracandler.com/filecabinet/math/PDF/Toe2ToeGeo.pdf>
Larson, Ron, Laurie Boswell, and Lee Stiff. "Congruent Triangles." Geometry: Concepts
and Skills. Evanston, IL: McDougal Littell, 2003. 233-39. Print
Le, Chau, Jane Lee, and Jennifer Lee. "Triangle Congruence Song." YouTube. YouTube,
27 May 2011. Web. 12 Apr. 2012.
<http://www.youtube.com/watch?v=_L8u8io6n2A&feature=related>
21
Paragraph Writing Rubric
3 2 1 Total
Main/Topic Idea
Sentence
Main/Topic
idea sentence
is clear,
correctly
placed, and is
restated in the
closing
sentence.
Main/Topic
idea sentence
is either
unclear or
incorrectly
placed, but is
restated in
closing
sentence.
Main/Topic
idea sentence
is unclear and
incorrectly
placed, and/or
is not restated
in the closing
sentence.
Supporting Detail
Sentences
Paragraph has
three or more
supporting
detail
sentences that
relate back to
the main idea.
Paragraph has
one or two
supporting
detail
sentences that
relate back to
the main idea.
Paragraph has
no supporting
detail
sentences that
relate back to
the main idea.
Accuracy of Content Information is
completely
correct; no
statements are
false
Information is
mostly
correct; 1or 2
statements are
false
Information is
not correct; 3
or more
statements are
false
Mechanics/Grammar Paragraph has
0-1 errors in
punctuation,
capitalization,
and spelling.
Paragraph has
2-4 errors in
punctuation,
capitalization,
and spelling.
Paragraph has
5 or more
punctuation,
capitalization,
and spelling
errors.
22
Section 5.1: Congruence and Triangles
Video Topics
Vocabulary
Corresponding Parts:
Congruent:
Notation
Writing a Congruent Statement
Step 1:
Step 2:
23
Are they congruent?
A. B.
C.
A.
B.
C.
Application
Example 1: Find the length of ̅̅ ̅̅ and the , given
Example 2: Determine whether the triangles are congruent. If so, write a congruence
statement.
Assignment
1
Annotated Bibliography
Abbott, E. A. (1928). Flatland: A romance of many dimensions. Cambridge: Cambridge
University Press.
Grades 9 and up
Flatland is a two-dimensional world in which geometric figures reside. The narrator is a
square who believes that other dimensions exist. The square’s main focus is to convince
Flatland’s monarch of the one-dimensional world, but becomes sidetracked when a
sphere appears to him. The square then goes off to explore this third dimension.
This book can be used in the Geometry class. This book will help students understand the
differences between one, two, and three dimension objects and the spaces they occupy.
This book can also help support literacy development of young adults because students
will be exposed to satirical writing. Students will be able to dig deeper into the reading to
see beyond the math terminology to realize that the author is criticizing social hierarchies
in the book.
Enzensber, H. M., & Heim, M. H. (2000). The number devil: A mathematical adventure. New
York: Holt.
Middle School
Robert is a young boy who does not understand math until the Number Devil begins
visiting him at night. The Number Devil teaches Robert mathematical concepts. Each
night Robert is exposed to different ideas. His outlook on mathematics begins to change
drastically due to his experiences in Number Heaven.
Various selections from this book can be used in a middle school classroom, Algebra, and
Geometry. The reason for this wide range is that Robert is exposed to topics that are
covered in each of those classes, such as prime numbers, Pascal’s Triangle, and
Euclidean Geometry. This book contains pictures, which not only give students a deeper
understanding, but also help keep the student’s interested in the read.
Fienberg, A. (2007). Number 8. New York: Walker.
Middle School
Jackson and his widowed mother, Valerie, move after his mother spotted her boss selling
drugs at the casino where she sang. He then befriends two of his talented neighbors,
2
Esmeralda and Asim. Although the family moved, Jackson suffers from anxiety about his
mother’s safety. He deals with his anxiety by obsessing over numbers. Things become
strained when Valerie’s boss sends a thug out to find her.
This book would be an excellent selection for those who are musically inclined, as all of
the major characters are talented musicians. This is also an easier read, so it may help the
struggling readers. This book could promote discussions over narration, as the chapters
are narrated by both Jackson and Esmeralda. This book would show a student that is
possible to have a love of numbers, just like Jackson. Finally, students would be drawn
into the plot through the thrilling and ominous events.
Flake, S. (2007). Money hungry. New York: Hyperion Paperbacks for Children.
Middle School
Raspberry Hill has grown up in the projects. Homelessness is not only known, it is a
reality for many around her. Her mother is attending school while still holding a job.
Raspberry wants nothing more than a better life for her and her mother. This desire
creates in her an extreme obsession with earning money. Raspberry must balance this
obsession with friendships and growing up.
A middle school math classroom would benefit from using this book during lessons about
money and earning interest. Students would be able to learn the importance of saving.
This could also work as an interdisciplinary piece. While students learn about the math
behind saving, they could also learn about the social issue of homelessness in social
studies. Money Hungry would promote literacy in the math classroom because students
would be able to draw on their knowledge of money while reading. Discussions could
ensue about alternative theories of how Raspberry could have handled her money,
drawing on what they have learned in the math classroom. Finally, this book would
expose students to a very different culture.
Griffin, A. (2004). Hannah, divided. New York: Hyperion Paperback.
Middle School
Hannah is an unstable thirteen year old. She suffers from a psychological disorder called
Obsessive-Compulsive Disorder. Hannah continually acts on her mathematical talents in
this way. Hannah and her family must work for the adults and children in her school to
accept her for her differences.
3
Hannah, Divided would be an excellent interdisciplinary tool. Math and psychology
students could both benefit from reading this book, as students could draw on their
schema to talk about math topics and mental disorders. This book could promote literacy
as it would generate various discussions about acceptance and friendship. This book
could also create an awareness of their metacognition. Students could discuss their
thinking as they do math and compare that to Hannah’s thoughts.
Halpin, B. (2008). Forever changes. New York: Farrar Straus Giroux.
Grades 9 and up
Briana is an eighteen year old suffering from cystic fibrosis. Although she is
mathematically talented, it does not matter to her because she does not think she will
make it to her graduation. Believing she is insignificant in the grand total of the universe,
she maintains a pessimistic outlook on life. Her senior year changes this, as she learns
about infinitesimal parts that can have significant effects on the system. Perhaps she is
not a nonentity after all.
This would be an excellent trade book for a Pre-Calculus or Calculus class as students
learn about limits. Forever Changes would give students a very different outlook on
infinitesimals and what they mean. Mathematical literacy would be promoted as it
exposes students to math vocabulary which they will see in the class used in real-life
situations. Students could discuss the connotation of the terms in the book and in the
classroom.
Hardy, G. (2001). A mathematician's apology. Cambridge: Cambridge University Press.
Grades 9 and up
G.H. Hardy was a man who began to feel the beginning of old age creep in. After a heart
attack, he could sense his mathemmatical creativity was dwindling. Thus, he felt a need
to write an essay, justifying his work in the mathematics field. He also talks about the
beauty of the mathematics field and his mathematical philosophy.
This nonfiction work would be great to have in a higher level math class. Students will be
exposed to the workings of a true mathematician’s mind. This is a shorter read; one that
students could finish within a week. This work would promote literacy because it is very
different from a novel or textbook. This was a work that was not necessarily written for
high school students, although the message may convince students to work on further
developing their math skills while they are young.
4
Moore, E. (1993). Whose side are you on? New York: Farrar Straus Giroux.
Middle School
Barbara is a struggling math student. When her mom decides to hire a tutor for her,
Barbara is shocked to discover that her tutor is T. J. Brodie. T.J. happens to be one of
Barbara’s oldest rivals. Despite past feelings, a friendship develops between the two.
When T.J. mysteriously disappears, Barbara is convinced T.J.’s grandfather is
responsible and decides to get to the bottom of the mystery.
Whose Side Are You On is a novel that would be a good read for struggling students, who
might relate to Barbara’s frustration with math. If this were a class assignment, it would
be a good idea to assign it during Black History month, as Barbara learns about African
American History throughout the book. Since this book is a mystery, students may
become engaged in the text. It would be helpful to hold discussions about predictions
while reading when trying to teach students literacy.
Scott, M. (1996). Gemini game. Mahwah: Troll.
Grades 3-5
Twins, Liz and BJ, invent a new virtual reality video game, Night Castle. When the game
becomes infected with a virus, the police go after them. The twins must enter the game
and find the source of the virus, before it is too late. While in the game, the twins
experiences adventures that they will never forget!
This is a novel for younger math students. 5th
graders may be able to see the applications
of mathematics and computer science. Some students may be inspired by the
protagonists’ innovation. The vocabulary used in this book assumes some knowledge of
computers and computer games. Students could re-write a shorter version of the book for
an audience with less awareness of the virtual reality world. This would allow students to
consider their audience when writing.
Stewart, I. (2006). Letters to a young mathematician. New York: Basic Books.
Grades 7 and up
Stewart writes to students about everything he wishes someone told him about
mathematics when he was younger. He explains to students why it is important to be able
to think mathematically. Not only does he write about what mathematics is, but also why
it is important for everyone to study. He talks about the future of mathematics, where he
5
thinks it is headed. Finally, he pokes a little fun at some of the quirks of the mathematical
community.
This is a book written specifically with math students in mind. Students who constantly
question the importance of math may find that Letters to a Young Mathematician has the
answers. This book would help students really understand that people in different fields
truly think in different ways. Those who have any interest in math at all, specifically
those who would like to further their career in mathematics will learn a lot from this
book. Literacy could be addressed by having students develop their writing. Each student
could write a letter about having success in mathematics, which could be brought
together in the form of a book. Students would need to pay particular attention to their
audience, tone and style. The writing process could also be discussed.
Literacy Action Plan Page | 29
The above elements will help me support the literacy development of my students. The
most important step in literacy instruction is planning. The interest inventory is a way to
determine how my students feel about math in general and what topics interest them. Knowing
this information will help me develop engaging lessons and assignments for my students. I can
apply this information when determining what articles or books I should have my students read.
Also involved in the planning stage is determining which textbook to use. Providing a
textbook that is well organized, informative, and an appropriate reading level will make
navigation of the text easy for students. Since the textbook will be the students’ primary reading
source, it is vital that the book will enhance their learning.
The lesson plans will help develop the literacy of my students as well. Each lesson begins
by going over key vocabulary words the students will encounter during the lesson. One lesson
includes an activity for students to understand the meaning of congruence. Writing is also
addressed in these lesson plans. I spend time explaining paragraph structure. Students are then
asked to construct a paragraph about what they learned during the class period.
The annotated bibliography will be extremely useful in my attempt to develop literacy in
my classroom. These books, or specific passages of these books, will provide more interesting
reads than a textbook. Many of the topics from the books will be taught in my classroom.
Students will be able to draw on their schema when reading these topics. Should I be unable to
incorporate some of these books into my lessons, they will be excellent additions to my
classroom library for students to read in their free time.
Literacy Action Plan Page | 30
[Additional References]
Interactive classroom technology. (2012). Retrieved May 10, 2012, from Adtech Systems:
http://www.adtechsystems.com/_Interactive_Classrooms.html
Kane, S. (2011). Literacy & learning: In the content areas (3rd ed.). Scottsdale, Arizona:
Holcomb Hathaways, Publishers, Inc.
Kenney, B. (2011, May 1). SLJ's 2011 technology survey: Things are changing. Fast. Retrieved
May 10, 2012, from School Library Journal:
http://www.schoollibraryjournal.com/slj/home/890197-
312/sljs_2011_technology_survey_things.html.csp
Lee, C., & Spratley, A. (2009). Content area literacy: Mathematics. Retrieved May 08, 2012,
from All About Adolescent Literacy: http://www.adlit.org/article/34643/
Rotherham, A. J., & Willingham, D. (2009, September). 21st century skills: The challenges
ahead. Retrieved May 08, 2012, from Educational Leadership:
http://www.ascd.org/publications/educational-leadership/sept09/vol67/num01/21st-
Schultz, D. (2008, February 27). Content area literacy: Beyond the language arts classroom.
Retrieved May 08, 2012, from Visual Thesaurus:
http://www.visualthesaurus.com/cm/teachersatwork/1305/
The James R. Squire Office of Policy Research. (2007). Adolescent literacy. Retrieved 2012,
from NCTE.org:
http://www.ncte.org/library/NCTEFiles/Resources/PolicyResearch/AdolLitResearchBrief
The Standards: English language arts standards. (n.d.). Retrieved May 10, 2012, from Common
Core State Standards Intiative: http://www.corestandards.org/the-standards/english-
language-arts-standards
